First, if the quilt is not too heavy you can roll it and hold it (never leave it alone) to watch it while it embroiders. Second, with the 3 layers of the quilt you don't need stabilizer, because it is stable enough. Last, either oregon patchwork or emblibrary.com have some patterns just for quilting that show in the front and the back exactly the same.
I would not attempt with a design that has satin stitches, but if the design is just for quilting, it will work.
Maria